With photovoltaic cells, you can use only as much as you want at any given moment and the surplus is just forgone. No ill effects.
Hydro and wind turbines however require a suitable load to control their speed. Without the load, they will simply speed up and up until they basically fly apart (or some other speed control kicks in - like a furling tail, or tap on the water line).
Batteries make a convenient way to capture power for later use - but if they are (or become) fully charged, or if they are not of sufficient capacity to take the full output of the turbine, then additional loads are required. So-called "opportunity loads" are often used - like large heating elements in hot-water units. If your water is already too hot, you'll need other places to use that power (or a way to shut down the turbine). Many people (myself included) have a large resistor "dump load" that is a last resort that the turbine controller can use to control the turbine.